Question

Can anyone prove the volume of an ellipse?

Answer 1

Do you mean find an area or actually prove the formula?

Answer 2

LOL can u read it?

Answer 3

yeah i can zoom in.

so basically they want you to use calculus to derive the formula for volume of a 3-d ellipse

Answer 4

yes :D

Answer 5

ok, start with equation of ellipse:

\[\frac{x^{2}}{b^{2}} +\frac{y^{2}}{a^{2}} = 1\]

then integrate from -b to b, of A(x) which is the area of each circular cross-section where the radius is y:
solve the ellipse equation for y
\[y = \sqrt{a^{2} - \frac{a^{2}}{b^{2}}x^{2}} = \frac{a}{b}\sqrt{b^{2}-x^{2}}\]